Math Problem Statement

Depreciation expense in the declining balance method

Solution

The declining balance method of depreciation is an accelerated depreciation method where an asset loses value more quickly in the earlier years of its useful life. Unlike straight-line depreciation, which allocates the same amount of depreciation each year, the declining balance method applies a constant depreciation rate to the book value (the asset's value at the beginning of the year after accounting for prior depreciation).

Formula:

Depreciation Expense=Depreciation Rate×Book Value at Beginning of Year\text{Depreciation Expense} = \text{Depreciation Rate} \times \text{Book Value at Beginning of Year} The depreciation rate is often double the straight-line rate in the double-declining balance method, which is one of the most common forms of this method.

Steps to calculate depreciation using the declining balance method:

  1. Determine the depreciation rate: For the double-declining balance method, the rate is 2useful life in years\frac{2}{\text{useful life in years}}.
  2. Calculate the book value at the start of the year: This is the asset's original cost minus any accumulated depreciation from previous years.
  3. Multiply the book value by the depreciation rate to get the depreciation expense for the current year.
  4. Subtract the depreciation expense from the book value to update the asset’s book value for the next period.
  5. Repeat this process for each year of the asset’s useful life, noting that the book value will decrease over time.

Example:

Suppose an asset costs $10,000, has a useful life of 5 years, and the company uses the double-declining balance method. The steps are:

  1. Straight-line rate: 15=20%\frac{1}{5} = 20\%, so the double-declining rate is 40%.
  2. Year 1 depreciation: 10,000×40%=4,00010,000 \times 40\% = 4,000, so the book value at the end of Year 1 is 10,0004,000=6,00010,000 - 4,000 = 6,000.
  3. Year 2 depreciation: 6,000×40%=2,4006,000 \times 40\% = 2,400, and so on.

The process continues until the book value is either fully depreciated or reaches a predetermined salvage value.

Would you like further details or examples on this?

Expanding Questions:

  1. What is the difference between the declining balance method and straight-line depreciation?
  2. How does the double-declining balance method compare to other accelerated methods like sum-of-the-years-digits?
  3. Can you explain the impact

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Math Problem Analysis

Mathematical Concepts

Depreciation
Accelerated Depreciation
Declining Balance Method
Double-Declining Balance Method

Formulas

Depreciation Expense = Depreciation Rate × Book Value at Beginning of Year
Depreciation Rate for Double-Declining Balance = 2 / Useful Life in Years

Theorems

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Suitable Grade Level

Undergraduate Finance/Accounting